NANO134 HW 5 - Darren Lipomi NANO/CENG/CHEM 134 Polymers HW #5 PDF

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Darren Lipomi NANO/CENG/CHEM 134 Polymers
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Rachel Miller

CENG/NANO(134( Homework(5( ( 1.! Consider(the(following(data(obtained(from(an(osmotic(pressure(“experiment”(at(room( temperature((T=300K):( ( 250

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Concentration((mol/cm3) ( ( a)! Calculate(the(number(average(molecular(weight,(Mn,(for(this(polymeric(system.( ( b)! Calculate(the(2nd(virial(coefficient,(B.(( ( ( ( ( ( ( ( ( ( ( (

2.! Consider(a(hypothetical(polymer(with(an(intermonomer(bond(length(of(7(Angstrom(and( a(chain(length(of(n(=(1000.(( a.! Assuming(the(polymer(chain(behaves(like(a(freely(jointed(chain,(calculate(the( average(radius(of(gyration(and(endYtoYend(distance(in(a(theta(solvent.( ( b.! Now(relax(the(assumption(of(a(freely(jointed(chain(and(assume(that(the( intermonomer(angle((θ)(is(constrained(to(70.5(degrees.(Compute(the(new( average(radius(of(gyration(as(well(as(the(ratio(of(this(new(value(to(that(of(the( freely(jointed(chain.( ( c.! Now(assume(that(the(intermonomer(dihedral(angles(follow(some(Boltzmann( distribution(such(that( !"#$ (=(0.5,(compute(the(new(radius(of(gyration(as(well( the(ratio(of(this(new(value(to(that(of(the(freely(jointed(chain.( ( d.! In(the(three(previous(cases(the(fact(that(monomers(can’t(physically(overlap(were( not(taken(into(account.(How(do(you(expect(the(excluded(volume(interactions(to( effect(the(average(radius(of(gyration?(( ( e.! (Find the value of the expansion factor, %,'for a freely jointed chain (part a) that will give the same radius of gyration as the hindered rotation model from part c. ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (...